A New Functional Setting for Term Structure Modeling Using the Heath–Jarrow–Morton Framework

Key findings from this study

• The authors propose that an unweighted functional space eliminates the interpretability problems associated with exponentially weighted settings in HJM modeling.
• The framework establishes that finite difference discretization combined with functional PCA enables effective calibration on real yield data.
• The study demonstrates that the proposed approach accommodates negative interest rates without structural modification.

Overview

The Heath–Jarrow–Morton framework models stochastic yield curve evolution under no-arbitrage conditions. Conventional implementations employ exponentially weighted function spaces whose parameters cannot be estimated from market data. This work introduces an unweighted functional space setting that addresses this limitation. Finite difference discretization yields a semiparametric model calibrated via functional principal component analysis on observed yield data.

Methods and approach

The authors discretize the HJM equation using finite differences. Model calibration employs functional PCA applied to real-world yield data. Backtesting and benchmarking compare the proposed framework against the one-factor Vasicek model. The analysis uses historical data spanning a period when AAA Euro Bonds exhibited negative yields, enabling assessment of the framework's capability to accommodate negative interest rates.

Results

The proposed unweighted functional space eliminates the arbitrary weight selection inherent in existing HJM implementations. This design permits objective interpretation of the functional setting parameters. The discretized semiparametric model demonstrates simulation capabilities for yield curve prediction and uncertainty quantification. Comparative analysis against the Vasicek model indicates competitive performance in backtesting exercises across the sample period.

Implications

Removing the weight parameter from the functional setting enables data-driven model specification without requiring external assumptions about decay rates or functional structure. This advancement improves the tractability of yield curve calibration in low or negative interest rate environments. The framework's flexibility extends HJM methodology to markets experiencing negative yields, broadening its practical applicability.

Scope and limitations

This summary is based on the study abstract and available metadata. It does not include a full analysis of the complete paper, supplementary materials, or underlying datasets unless explicitly stated. Findings should be interpreted in the context of the original publication.